Part c perfectly acceptable as long as we make our assumptions explicit. However weneed to be aware that, so far, the existence and properties of the real numbersis an assumption that has not been logically derived. Any time we make anassumption we need to be prepared to either abandon it completely if we findthat it leads to nonsensical results, or to re-examine the assumption in the lightof these results to see if we can find another assumption that subsumes the firstand explains the (apparently) nonsensical results.Additional ProblemsProblem 11. Determine if each of the follouing is always rational or alwaysirrational. Justify your answers.(a) The sum of two rational numbers.(b) The sum of two irrational numbers.(c) The sum of a rational and an irrational number.Problem 12. Is it possible to have two rational numbers, a and b, such that ais irrational? If so, display an erample of such a and b. If not, prove that it isnot possible.

Answered: Image /qna-images/answer/46b29143-4e5b-4ad0-bf64-76a80fab36c3.jpg

Math

Advanced Math

(c) (c) The sum of a rational and an irrational number.

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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